Question

What are the properties of Radioactive decay?

Answer 1

Hint: Radioactivity is the phenomenon of spontaneous disintegration of the nucleus of an atom with the emission of one or more penetrating radiation like alpha, gamma and beta rays. In order to understand the properties of a radioactive decay we first need to have the insight of the radioactive decay law. Further accordingly we will be able to determine the required properties.

Formula used:
$N={{N}_{\circ }}{{e}^{-\lambda t}}$

Complete step-by-step solution:
The radioactive decay law states that the number of nuclei disintegrating per second of a radioactive sample at any instant is directly proportional to the number of un decayed nuclei present in the sample at that instant. If ‘N’ is the number of radioactive nuclei present in the sample at time t, ${{N}_{\circ }}$is the number of nuclei at time t=0, then mathematically this can be represented as,
$N={{N}_{\circ }}{{e}^{-\lambda t}}$
Where $\lambda $ is the decay constant.
If we consider the above equation we can say that the following are the properties of a radioactive decay.
a) The number of active nuclei in a radioactive sample decreases exponentially with time. The rate of disintegration is faster at the beginning but becomes slower with passage of time.
b) Higher the value of decay constant, greater is the rate of disintegration at the beginning.
c) Irrespective of nature the radioactive samples will take infinitely long time to disintegrate completely.

Note:The decay constant gives us the probability per unit time that a nucleus of a radioactive sample will decay. The value of $\lambda $is dependent on the nature of the material. It is also to be noted that greater the decay constant, the half life for the sample is smaller.